62. Unique Paths

https://leetcode.com/problems/unique-paths/

Problem

A robot is located at the top-left corner of a m x n grid (marked 'Start' in the diagram below).

The robot can only move either down or right at any point in time. The robot is trying to reach the bottom-right corner of the grid (marked 'Finish' in the diagram below).

How many possible unique paths are there?

Example 1:

Input: m = 3, n = 7
Output: 28

Example 2:

Input: m = 3, n = 2
Output: 3
Explanation:
From the top-left corner, there are a total of 3 ways to reach the bottom-right corner:
1. Right -> Down -> Down
2. Down -> Down -> Right
3. Down -> Right -> Down

Example 3:

Input: m = 7, n = 3
Output: 28

Example 4:

Input: m = 3, n = 3
Output: 6

Constraints:

• 1 <= m, n <= 100

• It's guaranteed that the answer will be less than or equal to 2 * 109.

Solution

class Solution {
public:
    int uniquePaths(int m, int n) {
        int dp[m][n];
        for (int i = 0; i < m; ++i) dp[i][0] = 1;
        for (int i = 1; i < n; ++i) dp[0][i] = 1;
        for (int i = 1; i < m; ++i) {
            for (int j = 1; j < n; ++j) {
                dp[i][j] = dp[i - 1][j] + dp[i][j - 1];
            }
        }
        return dp[m - 1][n - 1];
    }
};

• #dp